The flux correction method combines unstructured flux correction along body surfaces and high-order finite differences normal to surfaces. This paper builds on previous twodimensional developments of the flux correction method and extends it to three-dimensional laminar and turbulent flow on strand grids. The development of flux correction scheme applied to three-dimensions is presented. Where turbulence modeling is required, a robust version of the Spalart-Allmaras turbulence model is employed that accommodates negative values of the turbulence working variable. A unique parallel communication strategy for high-order strand grid topologies is presented which eliminates the need for "fringe" nodes or cells in each partitioned block. A semi-implicit multigrid solution algorithm is described that allows for several advantageous solution techniques to be combined for optimal efficiency in terms of memory and computation time. Fundamental verification studies are conducted, which show the flux correction method achieves high-order accuracy for both laminar and turbulent flows. A three-dimensional steady-state study of a sphere is conducted over a range of laminar Reynolds numbers. The flux correction method accurately predicts the centers and length of recirculation vortices for each Reynolds number examined, and shows excellent comparison to experimental data. The three-dimensional unsteady capabilities of flux correction are displayed through a qualitative study of vortex shedding from a sphere.

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In this work, we examine the flux-correction method for three-dimensional transonic turbulent flows on strand grids. Building upon previous work, we treat flux derivatives along strands with high-order summation-by-parts operators and penalty-based boundary conditions. A finite volume-like limiting strategy is implemented in the flux-correction algorithm in order to sharply capture shocks. To achieve turbulence closure in the ReynoldsAveraged Navier-Stokes equations, a robust version of the Spalart-Allmaras turbulence model is employed that accommodates negative values of the turbulence working variable.Validation studies are considered which demonstrate the flux-correction method achieves a high degree of accuracy for turbulent shock interaction flows.